Collaborative Paper “Neuronal growth as diffusion in an effective potential” now published

We’re delighted to announce that our new paper, published in collaboration with Cristian Staii’s lab is now available online at Physical Review E. We’re particularly excited to congratulate undergraduate researchers Dan Rizzo (the first author!) and Matt Wiens on their first peer reviewed paper—well done!

On the left, a figure from the paper shows a microscope image of a neuron (the dark circular object on the right) with an axon extending from it (the wiggly line coming off it to the left). You can also see, at the far left, the brush-like object emanating from the axon is the growth cone which is responsible for guiding the axonal growth as it receives cues such as chemical signals from other neurons. As you can tell by the wiggliness of the axon, the growth is stochastic rather than deterministic, reminiscent of diffusion. Trying to determine the rules obeyed by the growth cone is complicated by the randomness. It’s as if Galileo had tried to observe grains of dust rather than cannon balls falling in his famous experiments—the simple rule that the acceleration is constant would be hidden by the random motion due to the air.

In the paper, we imaged the trajectories followed by the growth cones as they grew and, using a mathematical formalism for studying stochastic processes known as the Fokker-Planck equation, we were able to infer an effective guiding mechanism from the trajectories. Surprisingly, the velocity distribution did not follow the regular rule for diffusion like processes — which typically follows a Gaussian form — but instead appears to be a Laplace distribution. As we explain in the paper, this implies that the guiding mechanism that the growth cone uses is bistable — telling it to “speed up” if the velocity is below some value or “slow down” if it’s above.

The next step is to extend our model to incorporate how the neurons with external cues such as surfaces, etc. to guide the growth (as we showed was possible in an earlier paper) — this might help biomedical engineers trying to make artificial cortical tissue or doctors designing therapies to repair damaged nerves.